CSE331 Lecture 7

CSE331 Lecture 7 - Lecture 7 CSE 331 Online Office Hour...

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Lecture 7 CSE 331 Sep 13, 2011
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Online Office Hour today @9:45pm
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Access via the blog
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GS algorithm: Firefly Edition 1 1 2 2 3 3 4 4 5 5 6 6 Mal Wash Simon Inara Zoe Kaylee
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GS algo outputs a stable matching Last lecture, GS outputs a perfect matching S Lemma 2: S has no instability
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Two obervations Obs 1 : Once m is engaged he keeps getting engaged to “better” women Obs 2 : If w proposes m’ first and then to m (or never proposes to m ) then she prefers m’ to m
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Proof of Lemma 2 By contradiction m m w m’ w’ Assume there is an instability (m,w’) m prefers w’ to w w prefers m to m’ w’ last proposed to m’ w’ last proposed to m’
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Contradiction by Case Analysis Depending on whether w’ had proposed to m or not Case 1 : w’ never proposed to m w’ m w’ prefers m’ to m Assumed w’ prefers m to m’ Source: 4simpsons.wordpress.com By Obs 2 By Obs 2
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By Obs 1 By Obs 1 Case 2: w’ had proposed to m Case 2.1 : m had accepted w’ proposal m is now engaged to w Thus, m prefers w to w’ 4simpsons.wordpress.com
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This note was uploaded on 12/11/2011 for the course CSE 331 taught by Professor Rudra during the Fall '11 term at SUNY Buffalo.

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CSE331 Lecture 7 - Lecture 7 CSE 331 Online Office Hour...

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